For updated version, please click on http://ocw.ump.edu.my BSK1133 PHYSICAL CHEMISTRY CHAPTER 1 KINETIC THEORY OF GASES (PART A) PREPARED BY: DR. YUEN MEI LIAN AND DR. SITI NOOR HIDAYAH MUSTAPHA Faculty of Industrial Sciences & Technology yuenm@ump.edu.my and snhidayah@ump.edu.my
Description Aims To understand the properties of gases. To study the kinetic theory of gases.
Description Expected Outcomes Able to understand the properties and importance law of gases Able to understand the kinetic theory of gases at different properties changes References Atkins, P & Julio, D. P. (006).Physical Chemistry (8th ed.). New York: Oxford. Chang, R. (005).Chemistry (8th ed.). New York: McGraw Hill. Atkins, P & Julio, D. P. (01). Elements of Physical Chemistry (sixth ed.). Freeman, Oxford. Silbey, R. J., Alberty, A. A., & Bawendi, M. G. (005). Physical Chemistry. New York: John Wiley & Sons. Mortimer R. G. (008) Physical Chemistry, Third Edition, Elsevier Academic press, USA.
Contents 1.1 Gases and Its Properties 1. Gas Law 1.3 Gases Properties Calculation 1.4 Kinetic Molecular Theory Conclusion
1.1 Gases and its properties
Gases Elements that exist as gases at room temperature (5 0 C) and 1 atmosphere Sources: 01rc https://commons.wikimedia.org/wiki/file:periodic_table_large.png
Compressibility of Gases Unlike a liquid or solid which has its atomic particles in contact with one another, gas particles are far apart, colliding with one another and bouncing off in different directions. This means that a gas has no definite shape or volume and will expand to fill the container. Since gas has a great distance between its particles, gas has lower density as compared to solid or liquid; can be compressed.
Properties of Gases Property Description Unit(s) of Measurement Pressure (P) The force exerted by gas against the walls of the container Volume (V) The space occupied by the gas L, ml Temperature (T) Amount of gas (n) Determines the kinetic energy and rate of motion of the gas particles The quantity of gas present in a container atm, mmhg, torr, kpa C, K g, mol
Gas Pressure Gas particles are extremely small. Thus, billions of the gas particles will hit the walls of a container and exerts a force which known as pressure (Pressure = Force / Area). Sources: Olivier Cleynen and User: Sharayanan https://commons.wikimedia.org/ wiki/file:kinetic_theory_of_gas es_().svg The gas pressure is increased by increasing the frequency of collisions between gas particles and the walls of the container.
The frequency of collisions can be increased by: 1) Increasing the temperature of the gas: At higher temperatures, the movement of gas particles is faster and hitting the walls of container with more force and higher frequency. As a result, the gas pressure increases. ) Increasing the number of moles (n) (increasing the concentration of gas particles): Increasing the concentration of gas particles inside a container has resulted in increasing the collision frequency between the gas particles and the walls of the container; leading to an increase in the gas pressure inside the container. The unequal concentration of gas particles on either sides of the walls of the container causes a pressure differential to develop across the walls of the container.
Atmospheric Pressure: At the ground surface of the Earth, gravitation causes the column of air above it to exert a pressure equals to 1 atmosphere (atm). This pressure is defined as the atmospheric pressure. Mercury barometer can be use to measure the atmospheric pressure. The pressure of 1 atmosphere at sea level causes the mercury column in the barometer to rise to 760 mmhg (millimeters of mercury) high: 1 atm = 760 mmhg = 760 torr Sources: Volker Sperlich https://commons.wikimedia.org/wiki /File:Prinzip_Torricelli.jpg The mmhg is also known as the torr, named in honor of the Evangelista Torricelli who invented the barometer.
Unit Measuring Pressure: Unit Abbreviation Unit equivalent to 1 atm Atmosphere atm 1 atm (exact) Molimeters of Hg mmhg 760 mmhg Torr torr 760 torr Pounds per square inch Lb/in (psi) 14.7 psi Kilopascal kpa 101.35 kpa Unit SI : Pascal (Pa) 1 bar = 100,000 Pa
Effect of atmospheric pressure to altitude: Atmospheric pressure changes with altitude. As one ascends altitude, the air becomes less dense, causing lower atmospheric pressure. Conversely, in Death Valley, which is 8 feet below sea level, the air is denser and atmospheric pressure is greater. Location Altitude (km) Sea level 0 760 Los Angeles 0.009 75 Las Vegas 0.70 700 Denver 1.60 630 Atmospheric Pressure (mmhg) Mount Whitney Mount Everest 4.50 440 8.90 53 Sources: https://pixabay.com/en/landscape-mountainmountain-peak-186919/
Effect of atmospheric pressure to weather: Variations in weather also cause changes in atmospheric pressure. On a hot sunny day, the pressure on the mercury surface increases, causing the mercury column to rise to indicate a higher atmospheric pressure (weather report: high pressure system). Conversely, low pressure was found on a rainy day and the mercury column drops (weather report: low pressure system).
1. Gas laws
Boyle s Law : Pressure vs Volume In a piston-cylinder system, a movable, frictionless piston encloses an amount of n moles of a gas. When the volume of the gas decreases by one-half by compressing the cylinder, the pressure of the gas increases two-fold. This inverse relationship between volume and gas pressure is known as Boyle s law: P 1 V 1 = P V Product PV = Constant P and V show an inverse relationship. Conditions for Boyle s Law: 1) n moles of gas particles remain constant. ) temperature in chamber remains constant. Sources: OpenStax College https://commons.wikimedia.org/wiki/fil e:314_boyles_law.jpg
P 1/V P X V = CONSTANT P 1 X V 1 = P X V Constant temperature Constant amount of gas Sources: Krishnavedala https://commons.wikimedia.org/ wiki/file:boyles_law.svg f
Charles Law : Temperature vs Volume In 1787, Jacques Charles, a French physicist and a balloonist has proposed Charles law which stated that: The volume of a gas is directly proportional to the temperature (in Kelvin) at constant pressure and amount of gas (in moles). Charles law can be written as: V T or V 1 / / T 1 = V / T Temperature and Volume show a direct relationship. Conditions for Charles Law: 1) n moles of gas particles remain constant. ) pressure in chamber remains constant.
Sources: Physchim6 https://commons.wikimedia.org/wiki/file:char les%7s_law_graph.png V T V = constant x T Temperatures must be expressed in unit Kelvin. V 1 /T 1 = V /T f
Gay Lussac s Law : Temperature vs Pressure Gay-Lussac propounded a gas law that relates the temperature to the pressure of the gas; known as Gas-Lussac s Law: The pressure of a gas is directly proportional to its temperature (in Kelvin). Increasing temperature will increase the pressure of the gas, at constant volume and number of moles (n). P 1 / / T 1 = P / T Conditions for Gay Lussac s Law: 1) n moles of gas particles remain constant. ) volume of system remains constant.
Combined Gas Law The Combined Gas Law is the relationships among the conditions of pressure, volume and temperature for gases which the amount of gas (in moles) is remained constant. Combined gas law: P 1 V 1 / T 1 = P V / T
Avogadro s hypothesis stated that: Avogadro s Hypothesis Equal number of molecules consists of the same volumes of gases at constant temperature and pressure. V 1 / / n 1 = V / n Conditions for Avogrado s Law: 1) Temperature of gas particles remain constant. ) Pressure of system remains constant. Example:.414 L of any gas consists of 6.0 X 10 3 atoms (or molecules) at 1 atm and 0.
Dalton s Law Sources: https://ar.wikipedia.org/wiki/%d9%85%d9% 84%D9%81:Dalton%7s_law_of_partial_pres sures.png Dalton s Law of Partial Pressure states that the total pressure (P total ) for a mixture of unreactive gases is the sum of the partial pressures (P n ) of individual gases. P total = P 1 + P + P 3 + f
As shown in the figure: Tank A: hydrogen gas (H ) at.9 atm. Tank B: helium gas (He) at 7. atm. Tank C: total pressure of H + He is 10.1 atm. Sources: Dr. Blair Jesse Ellyn Reich https://commons.wikimedia.org/wiki/file:presiones_ parciales.jpg Condition: 3 tanks are same the volume and temperature. Number of gas molecules determines the gas pressure in a container regardless the type of gas. V and T are constant f
Example: Gas A and gas B are in a container of volume V P A = n ART V P B = n BRT V n A is the number of moles of A n B is the number of moles of B P T = P A + P B X A = n A n A + n B X B = n B n A + n B P A = X A P T P B = X B P T P i = X i P T mole fraction (X i ) = n i n T
Using Mole Fraction to Calculate Partial Pressure of A Gas: The partial pressures of the component gases in a mixture can be calculated by knowing the amounts (in moles) and the total gas pressure (P T ) of the gas mixture. Example: A gas mixture contains 3 different gases: A, B, and C. There are n A moles of A, n B moles of B, and n C moles of C. The total number of moles (n T ) of gases in a mixture, n T = n A + n B + n C Hence, the mole of the individual gas can be expressed as the mole fraction X: X A = n A = n A n A + n B + n C n T The partial pressure of gas component A, P A, can be determined by multiplying its mole fraction with the total gas pressure P T : P A = X A P T
Ideal Gas Equation Boyle s law: V 1(at constant n and T) P Charles law: V T (at constant n and P) Avogadro s law: V n (at constant P and T) V nt P V = constant x nt = R P nt P R is the gas constant
Boyle s Law : Increasing or decreasing the volume of a gas at a constant temperature. P = nrt 1 ; nrt is constant V Charles law: Heating or cooling a gas at constant pressure. V = nr P T; nr is constant P Heating or cooling a gas at constant volume. P = nr V T; nr is constant V Avogrado law: Dependence of volume on amount of gas at constant temperature and pressure. V = RT P n; RT is constant P Ideal Gas Equation: PV = nrt
The conditions 0 0 C and 1 atm are called standard temperature and pressure (STP). PV = nrt R = PV nt = (1 atm)(.414l) (1 mol)(73.15 K) R = 0.08057 L atm / (mol K)
1.3 Calculations
Density and Molar Mass Calculation Density (ρ) Calculations ρ = m V = PM RT m is the mass of the gas in g M is the molar mass of the gas Molar Mass (M ) of a Gaseous Substance M = ρrt P ρ is the density of the gas in g/l
1.4 Kinetic Molecular Theory
Postulates of the Kinetic Molecular Theory of Gases: 1. Small particles (atoms or molecules) in gas move rapidly and randomly. Gas molecules moving in all directions at high speeds cause a gas to fill the entire volume of a container.. The attractive forces between gas particles are negligible. Gas particles move far apart and expand to fill a container of any size and shape. 3. Gas molecules occupied very small volume compared to the volume that the gas occupies. Most of the volume of a gas is empty space, which allows gases to be compressible.
4. The average kinetic energy of gas molecules is directly proportional to temperature. Gas particles move faster as the temperature increases, hitting the walls of the container with more force and producing higher pressures. 5. Gas particles move in straight paths until colliding with other gas particles or with the walls of the container to bounce off elastically in other directions. An increase in either the frequency or force of collisions lead to an increase in the gas pressure.
Briefly kinetic model is based on three assumptions: 1) The gas exhibits random motion. ) The size of the molecules is negligible (much smaller than the average distance travelled between collisions). 3) The molecules interact through infrequent and elastic collisions.
v x v y v z v v x v x v x 3v x v x PV 1 3 v Nmv x 1 3 Nmv 3 N 1 ( mv ) Gas Pressure in the Kinetic Theory: PV 1 3 Nmv 1 3 nmv KE 1 mv P = gas pressure, V=volume v = mean square velocity N = number of gas molecules n = mole number of gas molecules = N/N A N A = Avogadro s number m = mass of the gas molecule M = molar mass of the gas molecule
Conclusion Gas particle is sensitively reacted to temperature, volume, pressure and number of mole changes. Gas has a specific condition at standard temperature and pressure (STP). Gas stoichiometry may relates to other properties of gases. Properties of gases can be identify using its mole concentration, density, molar mass. The speed of gas molecules can be determine using its kinetic theory of gases
AUTHOR INFORMATION DR. YUEN MEI LIAN (SENIOR LECTURER) INDUSTRIAL CHEMISTRY PROGRAMME FACULTY OF INDUSTRIAL SCIENCES & TECHNOLOGY UNIVERSITI MALAYSIA PAHANG yuenm@ump.edu.my Tel. No. (Office): +609 549 764 DR. SITI NOOR HIDAYAH MUSTAPHA (SENIOR LECTURER) INDUSTRIAL CHEMISTRY PROGRAMME FACULTY OF INDUSTRIAL SCIENCES & TECHNOLOGY UNIVERSITI MALAYSIA PAHANG snhidayah@ump.edu.my Tel. No. (Office): +609 549 094